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Compound Interest
Amount invested = £3000 Interest Rate = 4%
Interest at end of Year 1 = 4% of £3000
= 0.04 x £3000 = £120
Amount at end of Year 1 = £3120
Interest at end of Year 2 = 4% of £3120
= 0.04 x £3120 = £124.80
Amount at end of Year 2 = £3120 + £124.80
= £3244.80
and so on
Step-by-step Method
Amount invested = £3000 Interest Rate = 4%
Amount at end of Year 1 = 104% of £3000
= 1.04 x £3000 = £3120
and so on
Using a multiplier
Amount at end of Year 2 = 1.04 x £3120 = £3244.80
Try repeated calculations like this one on your calculator
Compound Interest
Compound Interest – Repeated Calculations
£3000 invested at 4% interest
End of Year n Amount A(£)
0 3000.00
1
2
3
4
5
3120.00
3244.80
3374.59
3509.58
3649.96
How much is in the account after 5 years?
Amount invested = £3000 Interest Rate = 4%
Using indices
Amount at end of Year n = 1.04n x £3000
Amount at end of Year 2
Amount at end of Year 5
= 1.042 x £3000
= 1.045 x £3000
= £3244.80
= £3649.96
What are the advantages and disadvantages of each method?
Compound Interest
DepreciationA new car costs £16 000
Age of car (n years) Value (£)
0 16 000
1
2
3
4
5
13 600
11 560
9826
8352
7099
What will it be worth when it is 5 years old?
What will the car be worth when it is 20 years old?
Its value falls by 15% per year
In this case the multiplier is 0.85
Falling Sales
Formula for annual sales n years from now
A company’s sales of a product are falling by 6% per annum.
Estimate the annual sales 6 years from now.
They sold 45 000 this year.
= 0.94n x 45 000
Estimate of annual sales 6 years from now = 0.946 x 45 000
about 31 000
Check this by repeated calculations.
In this case the multiplier is 0.94
Combining % Changes
Number after receiving 3% extra = 103% of 2000
= 1.03 x 2000
A shareholder owns 2000 shares.
How many shares will she have after these transactions?
She expects to get 3% more shares then plans to sell 25% of her shareholding.
= 2060
Number after selling 25% = 75% of 2060
= 0.75 x 2060 = 1545
What % is this of her original shareholding?
= 77.25% 1545
2000 100 or 1.03 x 0.75 = 0.7725
Combining other %
Sale Price = 75% of normal price
= 75% of 130% of cost price
A shop marks up the goods it sells by 30%
What is the overall % profit or loss on goods sold in the sale?
In a sale it reduces its normal prices by 25%
The shop makes a 2.5% loss on goods it sells in the sale
= 0.975 of cost price
= 0.75 x 1.3 x cost price
Reversing % Changes
1.025 x previous price = £66.42
Previous price
The price of a train fareincreased by 2.5% recently.
How much did it cost before the rise in price?
It now costs £66.42
Previous price = £64.80
= £66.42 1.025
Reversing % Changes
0.875 x full price = £25.90
Full price
After a 12.5% discount, the insurance costs £25.90
Full price = £29.60
= £25.90 0.875
What was the cost before the discount?
